Mechanisms and time scales of glacial inception simulated ... · ferent glacial inceptions with a...

Clim. Past, 5, 245–258, 2009www.clim-past.net/5/245/2009/© Author(s) 2009. This work is distributed underthe Creative Commons Attribution 3.0 License.

Climateof the Past

Mechanisms and time scales of glacial inception simulated with anEarth system model of intermediate complexity

R. Calov1, A. Ganopolski1, C. Kubatzki1, and M. Claussen2,3

1Potsdam Institute for Climate Impact Research, Potsdam, Germany2Max Planck Institute for Meteorology, Hamburg, Germany3KlimaCampus University Hamburg, Hamburg, Germany

Received: 15 January 2009 – Published in Clim. Past Discuss.: 24 February 2009Revised: 11 June 2009 – Accepted: 16 June 2009 – Published: 25 June 2009

Abstract. We investigate glacial inception and glacialthresholds in the climate-cryosphere system utilising theEarth system model of intermediate complexity CLIMBER-2, which includes modules for atmosphere, terrestrial veg-etation, ocean and interactive ice sheets. The latter aredescribed by the three-dimensional polythermal ice-sheetmodel SICOPOLIS. A bifurcation which represents glacialinception is analysed with two different model setups: onesetup with dynamical ice-sheet model and another setupwithout it. The respective glacial thresholds differ in termsof maximum boreal summer insolation at 65◦ N (hereafter re-ferred as Milankovitch forcing (MF)). The glacial thresholdof the configuration without ice-sheet dynamics correspondsto a much lower value of MF compared to the full model.If MF attains values only slightly below the aforementionedthreshold there is fast transient response. Depending on thevalue of MF relative to the glacial threshold, the transientresponse time of inland-ice volume in the model configura-tion with ice-sheet dynamics ranges from 10 000 to 100 000years. Due to these long response times, a glacial thresholdobtained in an equilibrium simulation is not directly appli-cable to the transient response of the climate-cryosphere sys-tem to time-dependent orbital forcing. It is demonstrated thatin transient simulations just crossing of the glacial thresholddoes not imply large-scale glaciation of the Northern Hemi-sphere. We found that in transient simulations MF has todrop well below the glacial threshold determined in an equi-librium simulation to initiate glacial inception. Finally, weshow that the asynchronous coupling between climate and

Correspondence to:R. Calov([email protected])

inland-ice components allows one sufficient realistic simula-tion of glacial inception and, at the same time, a considerablereduction of computational costs.

1 Introduction

Simulation of glacial inception with numerical models differ-ent in complexity and detail of description of climate com-ponents has already a long tradition. An early approachhas been undertaken by Weertman (1964) with an ice-sheetmodel based on the assumption of perfect plasticity in iceflow. Andrews and Mahaffy (1976) utilised an, at that time,relatively sophisticated two dimensional longitude-latitudevertically integrated ice-sheet model to simulate the Lauren-tide ice sheet dynamics. Common in these approaches is anextremely simplified representation of the surface mass bal-ance by mainly prescribing the movement of a so-called equi-librium line (height of zero mass balance). There are manyattempts to model glacial cycles, in particular glacial incep-tion, using conceptional models (Paillard, 2001; Saltzman,2002) which try to describe the entire climate system witha minimum set of ordinary differential equations. The ad-vantage of these models is that they are computational veryefficient. Due to large computational costs, simulations withGCMs (general circulation models of the atmosphere) so farwere restricted to time slices experiments (e.g. Dong andValdes, 1995; Yoshimori et al., 2002; Vettoretti and Peltier,2004) or, in case of transient simulations, tied up to rela-tive short integration time or asynchronous coupling (Pollardand Thompson, 1997; Vizcaıno et al., 2008). Earth systemmodels of intermediate complexity (EMICS; Claussen et al.,2002) are a compromise, because of their sufficient grade of

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246 R. Calov et al.: Mechanisms and time scales of glacial inception

complexity paired with adequate detail in description of theclimate subsystems. These models allow full synchronoustransient simulations over the time of decreasing boreal sum-mer insolation during glacial inceptions including all relevantcomponents of the climate system. In contrast to time slicesimulations, the transient approach captures adequately theinertia of the climate-cryosphere system, which will shownto be important in this paper.

One of the first EMICs including ice-sheet dynamics waspresented by Gallee et al. (1991). Wang and Mysak (2002)published a simulation of glacial inception with a geographi-cal explicit EMIC including interactive ice sheets (the McGillPaleoclimate Model). A number of feedbacks and mecha-nism in the context of glacial inception have been investi-gated with EMICs. One common results of different simula-tions is that the terrestrial vegetation amplifies glacial incep-tion (Kageyama et al., 2004; Wang et al., 2005; Kubatzki etal. 2006), mainly due the southward retreat of boreal forest(Calov et al., 2005b). A further, even more important processis the reduction of SSTs and expansion of sea ice, which leadto an additional strengthening of glacial inception (Wang andMysak, 2002; Calov et al., 2005b). Dust deposition on thesnow lowers the albedo of snow considerably (Calov et al.,2005a). This effect plays an important role for the ice coverin Alaska and north-east Eurasia, regions which mainly re-mained ice-free during the Quaternary. The importance ofdust deposition for the extent of the ice sheets during lastglacial inception was demonstrated by Calov et al. (2005b).GCM simulations which treated dust in snow-albedo param-eterisation resulted in a strong increase of snow free days peryear over Alaska and Northern Asia (Krinner et al., 2006),what supports the results yielded with an EMIC by Calov etal. (2005b). The disregarding of dust deposition could be thereason why many other modellers have a too expanded icecover over Alaska and north-east Eurasia.

Calov et al. (2005a) showed that glacial inception is pri-marily triggered by a drop in boreal summer insolation andis linked to a bifurcation from interglacial to glacial statecaused by snow-albedo feedback. They explicitly demon-strated the existence of two equilibria for the same forc-ing: one interglacial and one glacial equilibrium (bistabil-ity). Finally, Calov and Ganopolski (2005) found hysteresisin the climate-cryosphere system by tracing the space of Mi-lankovitch forcing. In this paper, we closer inspect glacialthresholds for model configurations with and without ice-sheet dynamics.

By Ruddiman (2003) and in further publications on thistopic (e.g. Ruddiman, 2007) it was postulated that earlyHolocene emission of greenhouse gases (GHGs) preventedlate Holocene glacial inception. Claussen et al. (2005) com-mented on Ruddimans’s hypothesis by comparing a transientsimulation through last glacial inception with a Holocenesimulation where Ruddiman’s postulated natural drop in at-mospheric CO2 applied. Here, we are widening Claussen’sapproach by treating Ruddiman’s hypothesised drop in atmo-

spheric CH4. We mimic the CH4 radiative effect with an ad-ditional drop in prescribed atmospheric CO2. But our resultsdo still not support Ruddiman’s hypothesis in the sense thateven an appreciable lowering of CO2 does not lead to notice-able glaciation of the Northern Hemisphere during the lateHolocene. The current minimum MF is close to the glacialthreshold and lowering of CO2 does affect this threshold. Butstill MF does not drop far enough below the glacial thresh-old to cause a late Holocene growth of the ice sheets over thecontinents of the Northern Hemisphere.

Further on, our analysis will support efforts to modelglacial inception with state-of-the-art Earth system mod-els. Due to high computation cost, GCMs so far can affordonly rather short integration times (some 1000 model years).Therefore, the use of asynchronous coupling is the only wayto perform transient simulations of the whole glacial incep-tion. Below, we investigate the influence of different asyn-chronous coupling strategies on the accuracy of transientsimulation of glacial inception.

The paper starts with the model description (Sect. 2) andan analysis of glacial thresholds (Sect. 3). The implicationfor the transient cryosphere-climate system if being subjectto a perturbation distant from the thresholds will be inspectedin Sect. 4. The investigation of transient response during dif-ferent glacial inceptions with a particular link to Ruddiman’shypothesis is included in Sect. 5. An analysis of the temporalcoupling properties of the climate and ice-sheet modules willfollow in Sect. 6. We close our paper with a discussion of ourfindings (Sect. 7) and conclusions (Sect. 8).

2 The model

The Earth system model of intermediate complexityCLIMBER-2 consists of an atmospheric part based on thestatistical-dynamical approach (Petoukhov et al., 2000). Theatmospheric component has a resolution of 10◦ in latitudeand about 51◦ in longitude. The atmosphere is coupled toa three-basin ocean model (similar to Stocker et al., 1992),which is run on a latitudinal resolution of 2.5◦ and resolves20 unequally thick layers in the vertical. The three basins arelinked in the circumpolar oceans. A thermodynamic sea-icemodel is included. The dynamical global vegetation modelVECODE (Brovkin et al., 2002) describes potential fractionsof tree, grass, and bare soil coverage. Land-surface processesare simulated on the spatial resolution of the atmosphericmodel. The original CLIMBER-2 model has been appliedto many types of climate studies, including the simulationof different palaeoclimates (e.g. Ganopolski et al., 1998a, b;Brovkin et al., 1999; Claussen et al., 1999; Rahmstorf andGanopolski, 1999; Kubatzki et al., 2000; Ganopolski et al.,2001).

In this paper, we utilise the upgraded model versionof CLIMBER-2 (Calov et al., 2005a), which includes thethree-dimensional polythermal ice-sheet model SICOPOLIS

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R. Calov et al.: Mechanisms and time scales of glacial inception 247

(Greve, 1997). The domain of SICOPOLIS is restricted tothe Northern Hemisphere extra-tropics in the given applica-tion. SICOPOLIS is run on a resolution of 0.75◦ in latitudeand 1.50◦ in longitude. It treats inland-ice extent, thickness,temperature, velocity, and water content. An interface mod-ule has been developed for direct bi-directional coupling be-tween SICOPOLIS and the coarse-resolution climate compo-nent of CLIMBER-2 described above. This coupler, SEMI,provides SICOPOLIS with annual values of surface tempera-ture and mass balance. SEMI interpolates the characteristicsit needs to determine the snow cover from the coarse atmo-spheric grid to the fine grid of the ice-sheet model taking intoaccount the high-resolution orography. It calculates snowthickness and surface temperature from this high-resolutioninformation using the same equations that are used in thecoarse-grid land-surface model. SEMI determines the an-nual surface mass balance of the ice sheets and passes it to-gether with the surface temperature to the ice-sheet model.The inland-ice model returns the updated values of inland-ice fraction, surface elevation, and sea-level back to the cli-mate model. For the calculation of snow albedo, variationsof the deposition of mineral dust were taken into account.For details see Calov et al. (2005a). In this work, we also usea model configuration without the ice-sheet model, but withthe area of inland ice diagnosed by SEMI on the spatial gridof the ice-sheet model.

CLIMBER-2 including the ice-sheet model has beenutilised for the simulation of Heinrich events (Calov et al.,2002) and transient simulations of last glacial inception(Calov et al., 2005a, b; Kubatzki et al., 2006). Calov andGanopolski (2005) used this model to perform a stabilityanalysis of the climate-cryosphere system in the phase spaceof MF, whilst Claussen et al. (2005) used this model to eval-uate a hypothesis by Ruddiman (2003) on the possible pre-vention of glacial inception during the late Holocene by earlyanthropogenic emission of CO2 and CH4.

3 Stability analysis

In order to better understand the mechanisms of glacial in-ception, we performed a stability analysis of the climate-cryosphere system in the phase space of MF similar to thatcarried out by Calov and Ganopolski (2005). We use twodifferent model settings for our stability analysis. In the firstsetting, we use the full CLIMBER-2 model including the ice-sheet model (ice-sheet dynamics “switched on” referred toas ID-on configurations hereafter). In the second setting, themodule which describes the ice-sheet dynamics is “switchedoff” (ID-off configuration). In the ID-off configuration, thesurface energy and mass balance interface SEMI is still en-abled and all land grid points where SEMI simulates positivesurface mass balance are treated as permanent snow coverarea. The area of permanent snow cover is then averaged overeach grid cell of the coarse resolution climate model and fed

back to the climate model as a time-dependent area of “inlandice”, one of six surface types considered in the CLIMBER-2 model. This surface type is characterised by high surfacealbedo equal to the maximum albedo of snow. Therefore,in the ID-off configuration the positive ice-albedo feedbackoperates the same way as in the ID-on configuration, but ad-ditional feedbacks associated with ice sheet lateral spreadingand elevation changes are ignored. The ID-off configurationis intended to emulate simulations of glacial inception withan AGCM (atmosphere only GCM) or an AOGCM (GCMof atmosphere and ocean) in absence of an ice-sheet model:a situation which often appeared for time-slice simulation ofglacial inception performed in the past (Syktus et al., 1994;Dong and Valdes, 1995; Gallimore and Kutzbach, 1996; deNoblet et al., 1996; Kageyama et al., 1999; Khodri et al.,2001; Yoshimori et al., 2002; Meissner et al., 2003; Vettorettiand Peltier, 2004; Kaspar et al., 2007). For both configura-tions, we use equilibrium interglacial climate as initial con-dition. While in the ID-on configuration the Greenland icesheet is allowed to evolve freely, the Greenland ice topog-raphy in the ID-off configuration is fixed to its present-dayvalue, because in the latter case no ice movement is possible.

To trace the equilibrium states of the climate-cryospheresystem, we slowly change MF for the whole range corre-sponding to the glacial-interglacial transition between 126and 115 kyr BP. We used here the method identical to that inCalov and Ganopolski (2005) except that we now vary MFby changing the precessional angle for fixed (large) eccen-tricity, while in Calov and Ganopolski (2005) we changedthe eccentricity for two different precessional angles. As itwas noted in Calov and Ganopolski (2005), a slow change inprecessional angle leads to a rather similar stability diagramin MF space as slow variation of eccentricity. We fixed theeccentricity and the obliquity of the Earth’s orbital param-eters to their respective values at 115 kyr BP ofe=0.04142andε=22.4◦, and the precessional angle (angle between ver-nal equinox and perihelion) was varied in negative directionfrom 90◦ to −90◦. Such a variation in the precessional an-gle corresponds to a lowering in MF, which causes a changefrom warm to cold Northern Hemisphere summer conditions.The atmospheric CO2 concentration is set to 271 ppm, whichcorresponds to its typical interglacial value prior to the onsetof glacial inception. The mineral dust deposition rate is setto its present day value according to Mahowald et al. (1999).

The precessional angle was changed such that it resultedin a linear change in MF. In the ID-on configuration, MFdecreases with a rate of 1.6×10−4 W m−2 yr−1 outside ofthe vicinity of the bifurcation transition from interglacial toglacial state. This rate was additionally reduced by a factorof 1/20 in the vicinity of the bifurcation transition, becausethe climate-cryosphere system needs longer time to equili-brate near the bifurcation point. The model in the ID-on con-figuration has been run for about 1.5 million model years totrace the stability diagram, whilst for the ID-off experimentwe used an order of magnitude larger rate of MF, because

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Fig. 1. Area of the Northern Hemisphere covered by ice sheets (inthe ID-off simulation area of positive surface mass balance) versusMilankovitch forcing (boreal summer insolation at 65◦ N, abbrevi-ated as MF) for CO2 concentration of 271 ppm. The area of theGreenland ice sheet is excluded. The curves originate from twosimulations with slowly varying MF: a run without ice-sheet dy-namics (ID-off configuration, long dashed line) and a run with icesheet-dynamics (ID-on configuration, solid line). The arrows showthe direction of climate-cryosphere system evolution in MF spaceunder slowly varying forcing. The filled circles denote inland-icearea from equilibrium ID-on simulations and the open circles fromequilibrium ID-off simulations. The vertical grey bars indicate theposition of the glacial thresholds in the ID-off configuration (SIDoff )and in the ID-on configuration (SIDon), respectively. The width ofthe grey bars is 1 W m−2.

in absence of ice-sheet dynamics the model has a muchshorter equilibration rate. Results of the stability analysis areshown in Fig. 1. Note that compared to Calov and Ganopol-ski (2005) we study here only that branch of the stability di-agram, which corresponds to the trajectory from high to lowMF. It has been shown in Calov and Ganopolski (2005) thatwith a gradual increase of MF the equilibrium trajectory doesnot follow the same path in MF space and that a pronouncedhysteresis exists. However, here we are only concerned withthe glacial inception and do not analyse the other branch ofthe stability diagram.

In addition to the method of slowly varying preces-sional angle, we performed a number of equilibrium simu-lations with fixed orbital parameters for certain values in MF(Fig. 1). In the ID-on configuration, these equilibrium sim-ulations were performed over 500 000 model years, while inthe ID-off configuration the model was run for 5000 years,which in both cases is sufficient to attain equilibrium stateswith high accuracy. These equilibrium simulations were per-formed to assess the robustness of our stability diagram ob-tained by gradual changes in MF, because it is not cleara priori how slow MF should be varied to trace the equilib-rium state of the climate-cryosphere system in the vicinityof bifurcation transitions. Near the glacial thresholds thechosen MF values of the equilibrium simulations differedonly by 1 W m−2. If of two neighbouring equilibrium sim-

ulations one reached glacial state and the other one stayedin interglacial state, then the MF of the simulation whichstayed in interglacial state was taken as the threshold valueof MF for the respective model configuration (see the greybars in Fig. 1). In Sect. 5, this technique is utilised to deter-mine the dependence of the ID-on glacial threshold on atmo-spheric CO2 concentration using CO2 values different fromthe 271 ppm which applies here.

For the ID-on configuration, it can be seen that near thebifurcation the MF of the equilibrium simulations does notfully lie on the curve from the method with slowly varyingparameter, which means that even such low rate of change ofMF in the vicinity of the bifurcation was still not sufficientlylow to trace the bifurcation point precisely. Although our bi-furcation analysis is worked out in the MF phase space, ourmodel computes the full orbital forcing in season and in lati-tude. The particular MF is chosen here, because our previouswork showed that MF is a good proxy for orbital forcing inthe context of interglacial to glacial changes (Calov et al.,2005a).

The glacial thresholds for the two model configurations(ice-sheet dynamics “on” and “off”) are well separated in MF(Fig. 1). For the ID-on model configuration, the critical valueof MF corresponding to transition from interglacial to glacialstate isSIDon=477 W m−2, which is only slightly below thepresent-day value (about 480 W m−2). The glacial threshold(by which we mean the appearance of large areas with posi-tive mass balance over the continents of the Northern Hemi-sphere) in the ID-off configuration isSIDoff =442 W m−2, farbelow SIDon and about to be as small as the minimum ofthe MF during last glacial inception (Fig. 5a). Obviously,the different positions of the glacial thresholds in MF spacearise from the fewer feedback mechanism in the ID-off con-figuration compared to the ID-on configuration. Mainly,there are three types of mechanism which originate fromthe cryosphere: ice/snow-albedo feedback, surface-elevationmass-balance feedback and expansion of inland ice throughice flow (ice spreading), of which only albedo feedback op-erates in ID-off configuration. In addition, the area of posi-tive surface mass balance in the ID-off simulation is notablysmaller in comparison with the inland-ice area in the ID-onexperiment for the same MF, which is again explained bymissing feedbacks related to ice-sheet dynamics.

4 Transient response to instantaneous change in orbitalforcing

Although useful for understanding of a nonlinear system,a stability diagram is not directly applicable to the transientresponse of the system. To investigate the time scale oftransient response of the climate-cryosphere system to time-dependent orbital forcing, we performed a set of experimentswhere we studied the model response (in ID-on configura-tion) to instantaneous changes of the orbital forcing. We



Fig. 2. Time series of inland-ice area of the Northern Hemisphereexcluding Greenland in 106 km2 and inland-ice volume in 106 km3

over 100 kyr in the simulation including ice-sheet dynamics (ID-on configuration) with constant orbital parameters correspondingto moderate (long dashed line, 460 W m−2) and low value of MF(solid line, 430 W m−2), respectively.(a) and(b) Inland-ice area;(c) and(d) inland-ice volume. The time axis is stretched by a factorof 200 in panels (a) and (c) compared to panels (b) and (d).

selected two sets of orbital parameters. One set yields a mod-erate MF equal to 460 W m2, which represents cold (com-pared to present-day orbital configuration) boreal summer.Another set of orbital parameters results in a low MF equalto 430 W m−2, which is due to extreme cold boreal summerconditions. The value of moderate MF is in betweenSIDoff

andSIDon, whilst the low MF is well below both glaciationthresholds. The moderate MF was obtained by prescrib-ing an eccentricity ofe=0.04142 and a precessional angleof ω=−32◦. For the low MF we used “cold” orbital con-figuration (i.e. precessional angle ofω=−90◦) and, in addi-tion, a high eccentricity ofe=0.05405. As initial conditionswe chose an equilibrium interglacial climate state (i.e. withGreenland ice sheet only) corresponding to present-day MF(i.e. 479.6 W m−2) and an interglacial CO2 concentration of271 ppm. Then we applied each of two orbital configurationsdescribed above and run the model for 100 000 years keepingCO2 and orbital parameters fixed, which is equivalent to in-stantaneous change of MF from the present one to “medium”or “low” value.

The time series of ice-sheet area, depicted in Fig. 2, exposean important difference in model response between moderateand low MF. While there is a fast response in inland-ice areawith a 13 million km2 increase during the first 100 years forlow MF, there is no visible increase in inland-ice area formoderate MF (Fig. 2a). The fast response to low MF cannotbe related to ice dynamics. A simulation without ice-sheet

dynamics (ID-off) under the low MF shows about the sameincrease in area of positive mass balance as the correspond-ing simulation with ice dynamics (not shown in the figure).Therefore, snow-albedo feedback has to play a major rolefor the initially fast increase in inland-ice area. While thearea and volume of the ice sheets increases very fast underlow MF and approach their equilibrium values already after20 000 years of integration, under moderate MF only rathersmall ice sheets are formed during this period of time andonly after 20 000 years of integration the growth of the icesheets accelerates considerably (Figs. 2 and 3). Note that theequilibrium state does not differ much between these two MFvalues.

The main differences in the initial phase of ice-sheetgrowth between moderate and low MF are illustrated with anice-thickness plot (Fig. 3). While there are only rather smallareas in the high north glaciated after 100 years in the sim-ulation with moderate MF, a thin ice field with a thicknessof about 10 m covers about half of the North American con-tinent after the same model time under low MF (Fig. 3a, d).After 10 000 model years, there are small and relative thickice caps in the high north for moderate MF, while there areabout fully developed large ice sheets in North America andNorthern Eurasia for low MF (Fig. 3b, e). At the end of thesimulations, the ice thickness distribution for moderate andlow MF is similar showing two big ice sheets in North Amer-ica and Northern Eurasia (Fig. 3c, f).

In the following, we would like to further inspect thephases of ice build up. For moderate MF, one can detect threephases in ice-sheet build up: an initial ice-spreading phase(or spreading-only phase), when due to rather small sizedice caps, the ice-albedo feedback plays little role, a termi-nal relaxation phase and a transitional phase in between. Forboth, the initial und the terminal phase we developed a simplemodel, which we compare with our CLIMBER-2 simulationsin the ID-on model configuration. The ice-spreading model(Appendix A) assumes a small quasi-equilibrium axisym-metric ice sheet, which grows under constant positive sur-face mass balance. The even simpler relaxation model (Ap-pendix B) just assumes relaxation to an equilibrium inland-ice volume with a time constant in an exponential function.A pronounced spreading phase during the initial phase ofice build-up can only be seen in the inland-ice volume curvewith moderate MF, higher thanSIDoff , because for lower val-ues of MF, the ice-albedo feedback plays an important rolefrom the beginning. To test the robustness of our conceptualmodels, we performed two additional runs with MF equal455 and 465 W m−2. The spreading and relaxation phasesof the three equilibrium simulations are shown in Fig. 4. Itcan be seen that in all three simulations the second derivativeof the inland-ice-volume curves changes its sign from posi-tive (concave shape) for the spreading-only phase to negative(convex shape) for the relaxation phase (Fig. 4). The concaveshape of the volume curve is reproduced by the power law ofEq. (A9) and the convex shape by an exponential relation



Fig. 3. Simulated ice-sheet thickness (in m) for different phases of ice build up under constant MF. Comparison of response to moderate MF460 W m−2, panels(a–c)and low MF value 430 W m−2, panels(d–f) at 0.1 kyr (a and d), 10 kyr (b and e) and 100 kyr (c and f) after thebeginning of the experiments.

Fig. 4. Inland-ice volume of the Northern Hemisphere excludingGreenland in 106 km3 vs. simulation time in kyr. The black curvesare from simulations with CLIMBER-2. The numbers above theblack curves indicate the values of the MF. The red and blue curvesare based on a simple ice-spreading model and a simple relaxationmodel, respectively.

(Eq. B1). In all three cases for the spreading model we usethe same constant surface mass balance of 0.3 m yr−1 andfit the simple model to CLIMBER-2 simulations by choos-ing initial ice volumesV1 and time offsett1 in Eq. (A9).The relaxation time in Eq. (B1) is set to 17 000 years for allthree experiments and the relaxation model was fitted to theCLIMBER-2 results by choosing appropriate initial ice vol-umeV2 and time offsett2 in Eq. (B1). Figure 4 shows thatthe ice spreading model is applicable only for rather small ice

Table 1. Transient simulations and their time domain. BP abbrevi-ates before present and AP abbreviates after present.

Stage/notation of simulation Time domain

MIS 1 11 kyr BP to 14 kyr APMIS 5 128 to 100 kyr BPMIS 11 410 to 385 kyr BP

volumes, whilst the relaxation model describes quite satisfac-torily the inland-ice-volume evolution after it reaches abouthalf of its equilibrium value.

5 Transient response to realistic orbital forcing

In the following, we investigate the transient response of theclimate-cryosphere system to realistic time-dependent orbitalforcing (Berger, 1978) corresponding to the marine isotopicstages 1, 5 and 11 (MIS 1, 5 and 11). The simulations startat times of maximum MF, pass one minimum in MF and goon towards the next maximum in MF (Table 1, Fig. 5a). Forthe chosen time interval, we performed simulations with twodifferent values in atmospheric CO2 concentration. The CO2values were fixed to 280 and 220 ppm, respectively, through-out the entire simulations. In all experiments we used inter-glacial equilibrium state as initial conditions.

Figure 5, displays time series of MF and inland-ice vol-ume simulated under MIS 1, 5 and 11 orbital forcings. TheMF during MIS 1 has a rather weak minimum, the MF min-imum during MIS 5 is much stronger and the MIS 11 in-solation minimum is approximately in between the MIS 1and MIS 5 minima (Fig. 5a). The glacial thresholds for220 and 280 ppm atmospheric CO2 concentration shown in



Fig. 5a are determined using the same technique as describedin Sect. 3. It can be seen that these two glacial thresholdsof SIDon(220)=486 W m−2 andSIDon(280)=476 W m−2 differonly by 10 W m−2. Such a dependence of MF on atmo-spheric CO2 concentration agrees well with results by Archerand Ganopolski (2005).

The transient simulations show pronounced glacial incep-tion during MIS 5 for both atmospheric CO2 concentrationswhich were applied here. Glacial inception is indicated bya strong increase in inland-ice area (Fig. 5b). In the tran-sient MIS 5 simulation with 280 ppm atmospheric CO2 con-centration, glacial inception appears about 2500 years laterand with about 40% less maximum inland-ice area comparedto 220 ppm. The situation differs for the MIS 11 simula-tion: an appreciable increase of inland-ice area occurs for220 ppm CO2 concentration but not for 280 ppm. Finally, forMF corresponding to MIS 1 (including the future) extremelysmall changes in inland-ice area are simulated for both 220and 280 ppm atmospheric CO2 concentration, i.e., our modeldoes not simulate glacial inception during MIS 1 even fora rather low CO2 level.

Figure 5a illustrates the complex relationship betweencrossing of glacial thresholds and the onset of glacial in-ception. During MIS 5 the MF drops far below the glacialthresholds for both CO2 concentrations and there is alwaysa strong glacial inception (Fig. 5b). But during MIS 1 andMIS 11 model response is different: considering the positionof the insolation minima relative to the glacial thresholds, itis tempting to conclude that there should appear glacial in-ception during MIS 11 for CO2 values of 280 ppm and thatthere would be glacial inception for MIS 1 for an atmosphericCO2 concentration of 220 ppm. However, this conclusion isnot supported by modelling results, which show that a smalland short-term drop of MF below the glacial threshold is notsufficient to initiate glacial inception. Indeed, with ahalf pe-riod of about 10 000 years, the orbital precessional forcing isstill too fast compared to the time scales of initial ice spread-ing discussed in the previous section. Our transient simula-tions indicate that MF has to drop below the glacial thresh-old by about 20 W m−2 to cause the onset of the NorthernHemisphere glaciation. This value emerges from analysisof the MIS-11 simulations: for the difference of 15 W m−2

between the glacial threshold for 280 ppm CO2 and the min-imum in the MIS-11 MF, our transient simulation does notshow a pronounced glacial inception. But there is successfultransient simulation of glacial inception for the difference of25 W m−2 between the same MF minimum and the glacialthreshold for 220 ppm CO2. From additional MIS-11 simu-lations with 240 and 260 ppm atmospheric CO2 concentra-tion (not shown in a figure), we found that a drop of about20 W m−2 below the glacial threshold is needed to initiateglacial inception. Certainly, the value which MF has to fallbelow a glacial threshold to initiate glacial inception couldbe different for MIS 1, MIS 5 and MIS 11, because e.g. thedecrease rate in MF varies for these marine isotopic stages.

Fig. 5. Time series during MIS 1, MIS 5 and MIS 11. The time axesare relative to the times of the relative minima of Milankovitch forc-ing (MF). MFmin=0.5 kyr for MIS 1,−115.8 kyr for MIS 5,−398.5for MIS 11. (a) Milankovitch forcing (maximal boreal summer in-solation at 65◦ N) in W m−2. The thin solid lines indicate com-puted glacial thresholds for 220 and 280 ppm atmospheric CO2 con-centration.(b) Inland-ice area of the Northern Hemisphere exceptGreenland in 106 km2 during MIS 1 for 220 ppm (thick red curve)and 280 ppm (thin red curve) atmospheric CO2 concentration, dur-ing MIS 5 for 220 ppm (thick blue curve) and 280 ppm (thin bluecurve) atmospheric CO2 concentration as well as during MIS 11for 220 ppm (thick orange curve) and 280 ppm (thin orange curve)atmospheric CO2 concentration.

6 Asynchronous coupling of climate and ice-sheetcomponents

Due to high computational costs it was not possible so far toperform transient simulations of glacial inception with com-plex Earth system models (AGCMs, AOGCMs). This prob-lem, however, can be circumvented by using an accelerationtechnique. The concept of acceleration is based on the fact



Fig. 6. Illustration of different coupling procedures. The horizontalaxes count the model years beginning at an arbitrary model yearn

in the simulation. The vertical arrows show the direction of dataflow. tC andP denote the climate-module-computation time andthe time interval of information exchange, respectively. The val-ues of tC and P , on which the figure is based, are examples toshow the principle.(a) Synchronous coupling with yearly data ex-change (tC=1 year,P=1 year). (b) Asynchronous coupling withtC=2 years andP=6 years. The dashed line indicates an interrup-tion in calling the climate module. This results in an accelerationA=P/tC=3, which implies that computation costs of climate com-ponent is reduced by factor three compared to the fully interactiverun.

that typical time scales of the most computationally expen-sive components of complex Earth system models, the oceanand the atmosphere, are much shorter than the orbital timescales. This allows one to reduce run-time of the climatecomponents of an Earth system model by an artificial accel-erating of the external forcings, namely, orbital and GHGs.For example, acceleration by a factor of ten would implythat a transient run representing changes in orbital forcingand GHGs from 120 to 110 kyr BP would require only onethousand years of run-time of the climate component. Un-like the climate component, the ice-sheet module cannot beaccelerated in the same manner, because the time scale of icesheets is comparable with the orbital time scales. This, how-ever, does not represent a problem, because current ice-sheetmodels are computationally relatively inexpensive comparedto the AOGCMs and can be run without acceleration on the

orbital time scale. The practical question is how much the cli-mate component can be accelerated to produce still a realis-tic simulation of glacial inception. The CLIMBER-2 model,due to its sufficient degree of realism and low computationalcost, is a useful tool to address this question.

Below, we compare results of several accelerated runs withthe reference run, where climate and ice-sheet componentsexchange information every year (Fig. 6a). An additionalproblem which arises for acceleration technique is relatedto large (and realistic) interannual climate variability sim-ulated by AOGCMs. When the climate component is ac-celerated, for example, by factor of ten, the mass balancesimulated in the climate component for a single year willbe applied to the ice-sheet components over ten consecutiveyears, thus producing unrealistic high interdecadal variabil-ity in the mass balance. In a view of a strong nonlinearityof the ice-sheet component, it may cause additional biases inthe simulation of ice-sheet dynamics. The most straightfor-ward way to suppress this effect is to run the climate modelfor several consecutive years and use mass balance, whichis averaged over this period of time, to drive the ice-sheetmodel. This will substantially reduce variability in the ice-sheet’s forcing. If we denote the period of time which isused to reduce the temporal noise in climate model outputby tC and the acceleration factor byA, then the time inter-val of information exchange between climate and ice-sheetcomponents will beP=tCA (Fig. 6b). Therefore, this tech-nique for a given acceleration factor will increase the intervalof time of information exchange between climate and ice-sheet components. For example, for the acceleration factorA=10 and the averaging period of mass balancetC=10 yr,the exchange between ice-sheet and climate component willoccur only once per hundred years of the ice-sheet model,which, again, can disturb the simulation of glacial inception.Since the CLIMBER-2 model does not produce realistic in-terannual variability, we cannot assess the effect of interan-nual variability on simulation of ice sheet growth in the ac-celerated runs. But we can assess the effect of reduction ofcoupling frequency associated with the averaging of climatemodel output over several years.

Here, we present a set of transient simulations of lastglacial inception with different acceleration and time cou-pling parameters. In these simulations, the model wasforced by atmospheric CO2 concentration from Petit etal. (1999) and the Earth’s orbital parameters according toBerger (1978). Equilibrium interglacial climate state servesas initial condition and the model was run from 128 to100 kyr BP. Figure 7 compares simulated sea level duringlast glacial inception in experiments with different couplingparameters. Comparison of simulated sea level in the syn-chronously coupled run (P=1 yr, A=1, denoted in Fig. 7 as“run 1/1”) with proxy data was already presented in Calovet al. (2005b) and is rather satisfactory. Simulated sea levelis only slightly higher in run 30/3 (P=30 yr, A=3) com-pared to run 1/1. With a further increase of the time interval



Fig. 7. Simulated contribution of the ice sheet of the NorthernHemisphere to sea level variation during last glacial inception. Thesimulations have been performed with different coupling parame-ters. Ratios denote setup of the simulations: “time interval of in-formation exchange”/“acceleration”, e.g., for the solid red line theinformation exchange interval is 1000 yr and the acceleration is 100.

of information exchange in run 100/10 the deviation in sealevel relative to the reference run is already clearly visiblebut qualitatively results are not very different. An informa-tion exchange interval of 1000 yr leads to extreme reductionin simulated sea level drop, which shows that such an infor-mation exchange interval is too long for realistic simulationof glacial inception. To quantify the quality or accuracy ofthe accelerated climate-cryosphere coupling, we performeda suite of experiments with a broad range of information ex-change intervals and accelerations. As quality criterion, wechose the ratio of simulated inland-ice volume in acceleratedruns to the reference run at 110 kyr BP. This ratio, measuredin percentages, is shown in Fig. 8. The simulations show thattime intervals of information exchange between 1 and 100 yrand accelerations inside the interval 1 to 10 result in a ratiobetween 85 and 100%. An increase of the information ex-change interval beyond 300 and/or accelerating the climatemodule more than thirty fold lead to a quality ratio of lessthan 60%. The latter is not surprising, because such accel-eration factors reduces the time scale of accelerated orbitalforcing to the same order as the time scale of the compo-nents of the climate system. However, the fact that an accel-eration by factor ten still enables to perform a relatively ac-curate simulation of glacial inception suggest that simulationof glacial inception with an AOGCM coupled to a ice-sheetmodel can be performed already with the current generationof supercomputers.

Fig. 8. Isolines of ratio of ice volume to reference ice volume (run1/1) at 110 kyr BP in percentages. The grey area marks settingswhen the climate-module-computation time becomes smaller than 1year (one seasonal cycle).

7 Discussion

Our simulated glacial threshold in the MF space in themodel configuration without ice-sheet dynamics correspondsto a much lower value of MF compared to that in the modelexperiment with ice-sheet dynamics. This has important im-plications for simulations of glacial inception with AGCMsor AOGCMs. Glacial inception in AGCMs/AOGCMs whichdo not include inland-ice dynamics can occur only for muchlower MF than in models which do include cryosphere dy-namics, because the ID-off threshold is considerably lowerthan the ID-on threshold (Fig. 1). In realistic transient sim-ulations of glacial inception interactive ice-sheet dynamicshave to be considered.

For constant MF values betweenSIDoff and SIDon thegrowth of the ice sheet is characterized by three distinctivephases. Although results from both the simple ice-spreadingmodel and the relaxation model agree only passably withthose from CLIMBER-2, we think that these two simplemodels together reproduce first order effects of ice buildup. The two simple models together and CLIMBER-2 ex-hibit a pronounced change in sign of the second derivative ofthe inland-ice volume. Further on, the increase of inland-icevolume of the simple spreading model strongly depends onthe initial inland-ice volume, which, in turn, depends on theinitial land area with positive mass balance. This explainswhy duration of the spreading phase is so sensitive to thevalue of MF (Fig. 4). If the MF is below the value ofSIDoff ,no spreading phase exists, because snow-albedo feedback isstrong enough to produce a large area of permanent snowcover over centennial time scale. In this case, the glaciationof the Northern Hemisphere proceeds much faster and largeice sheets can be formed on precessional time scales.

A threshold in our understanding is strictly tied to a sys-tem in equilibrium and, accordingly, our stability diagram



(Fig. 1) is determined with quasi-equilibrium simulations ap-plying slowly varying forcing or, alternatively, with a set ofpure equilibrium simulations. This choice is due to the factthat a unique determination of a threshold is impossible viatransient simulations, because such a “threshold” will dependon the rate of change of the forcing. The sudden strong in-creases in ice area in the transient simulations seen in Fig. 5b(e.g. at about−4 kyr from MFmin in the run through MIS 5with 220 ppm CO2) do not correspond to any glacial thresh-old. The time scale of initial spreading of the small ice capsin the high North can be rather large compared to the timescale of precession (Fig. 4). During the first some thou-sand years, the curves of inland-ice area in Fig. 5b have asimilar characteristics as the ice-volume curves in Fig. 4,which are shown to indicate ice spreading. The strong in-creases in inland-ice area seen for the MIS 5 and MIS 11simulations appear at those times when snow albedo feed-back starts to contribute strongly to cooling. The timingof the strong increase in inland-ice area is a race betweenice spreading, which gradually brings cooling in the systemthrough albedo, and the change in MF, which will eventuallystart do increase after reached its minimum. It also dependson how deep and how fast the MF decreases. If MF does notreach deep enough (about 20 W m−2, see Sect. 5) below theglacial threshold, there is no glacial inception in the sense ofwidespreadglaciation as found in geological records.

Our simulations of glacial inceptions shed new light ona debate (Claussen et al., 2005; Crucifix et al., 2005)on the overdue Holocene glaciation hypothesis by Ruddi-man (2003). As response, Ruddiman (2007) mentioned thatClaussen et al. (2005) as well as Crucifix et al. (2005) did notapply his hypothesized drop in CH4 in addition to the CO2decrease. Claussen et al. (2005) used only a CO2 drop to240 ppm, a value which was proposed by Ruddiman (2003).With the atmospheric CO2 equivalent of 220 ppm, which weused in our simulations, we safely accounted for the radia-tive effect of the CH4 drop from 700 to 450 ppb, which wasproposed by Ruddiman. Such a decrease in methane corre-sponds to an additional radiative forcing of about 0.3 W m−2,which follows from an empirical formula by Houghton etal. (1995) and usage of the efficacy of 1.4 by Hansen etal. (2005). This additionally radiative forcing of 0.3 W m−2

can be mimicked by a further drop in atmospheric CO2 from240 to 227 ppm. Still, even if we keep constant the 220 ppmCO2 concentration during the whole Holocene (includingnext 10 000 yr), only a minute increase of the Northern Hemi-sphere ice area occurs even though MF drops below glacia-tion threshold for this CO2 concentration over several thou-sand years. Therefore, during stage 1, unlike stages 5 and 11,the drop in CO2 does not affect qualitatively model resultsand does not lead to the appreciable glaciation of the North-ern Hemisphere. This is explained by the fact that due toa low eccentricity, the minimum of MF during MIS 1 is un-usually weak and not sufficient to cause onset of glaciation.

By fixing eccentricity and obliquity under varying preces-sional angle, we opted for a rather artificial forcing in ourstability analysis. Another possible procedure is to apply thereal orbital forcing and, most important, slow down this forc-ing considerably. Again, slow change in the forcing is the keyelement in such an analysis.

Using the CLIMBER-2 model, we analysed the accuracyof simulation of the last glacial inception for different accel-eration strategies. Under accuracy we understand here thedegree of agreement between fully synchronous and accel-erated runs. We found that this accuracy depends on boththe acceleration factor and the time interval of informationexchange. Our results demonstrate that for acceleration fac-tors up to ten and exchange intervals of up to 100 yr (whichimplies averaging of mass balance over ten model years),the accuracy of simulation of glacial inception remains rea-sonably good, which indicates that the acceleration tech-nique can reduce considerably computational costs of tran-sient simulation with complex Earth system models.

It should be noted that in our simulations we do not includethe carbon cycle. As it was shown by Brovkin et al. (2007),the time scale of response of the marine-carbon system tochanging boundary conditions is several thousand years, i.e.,it is longer than that of the physical components of the cli-mate system. This fact can impose an additional constrainton the maximum possible acceleration of a comprehensiveEarth system model, but this question is beyond the scope ofthis paper.

8 Conclusions

1. Two glacial thresholds are determined in differentmodel setups of CLIMBER-2. The value of thesethresholds depends also on the CO2 concentration of theatmosphere (Fig. 5a). For 271 ppm atmospheric CO2concentration, the glacial threshold in the model con-figuration without ice-sheet dynamics corresponds toa very low MF value of 442 W m−2, while the glacialthreshold in the model configuration with ice-sheet dy-namics relates to a MF value of 477 W m−2, whichis only slightly smaller than the present-day value inMF. Supposedly, the low threshold applies rather forAGCMs and AOGCMs where ice-sheet dynamics is notaccounted for.

2. For moderate forcing (MF around 460 W m−2, CO2concentration of the atmosphere 271 ppm), theCLIMBER-2 model with inclusion of ice-sheet dynam-ics exhibits rather long transient response times, whichare related to initial spreading of small ice caps in thehigh north. The duration of this initial phase dependsstrongly on the value of MF. Because of the rather slowresponse of the climate-cryosphere system, a drop ofMF of about 20 W m−2 below the glacial threshold isnecessary to produce substantial glaciation during one



precessional cycle. This implies that transient glacialinception, in the sense of glaciation of vast areas ofthe Northern Hemisphere, happens thousands of yearslater than the time of crossing the glacial threshold.We would like to stress that (glacial) thresholds cor-respond to a system in equilibrium and just crossingof the glacial threshold does not imply instantaneousglaciation of the Northern Hemisphere.

3. We demonstrated with transient simulations applyingextreme scenarios in drop of CO2 equivalent that glacialinception during the Holocene is all but impossible, be-cause the MF does not drop far enough below the glacialthreshold irrespectively of CO2 concentration. In con-trast, during MIS 5 and MIS 11 CLIMBER-2 is able tosimulate transient glacial inception with reasonable val-ues in CO2 equivalent. Therefore, our results do notsupport Ruddiman’s overdue Holocene glaciation hy-pothesis.

4. With CLIMBER-2 we investigate the consequences ofasynchronous coupling of climate models with ice-sheetmodels. Our results are thought to be applicable to com-plex (AOGCM-based) Earth system models which in-clude an ice-sheet component. In particular, an acceler-ation of climate component by up to the factor ten givesgood agreement with the full synchronous simulationof glacial inception, whilst for higher acceleration fac-tors the model underestimates considerably the growthof ice sheets during glacial inception. This result indi-cates that utilisation of asynchronous coupling in princi-ple permit realistic simulation of glacial inception withcomplex Earth system models already with the existingcomputers performance.

Appendix A

Ice spreading in a quasi-equilibriummathematical approach

Here, we would like to derive a simple relation for the depen-dence of inland-ice volume on time during the initial spread-ing phase of ice. We assume that small ice caps evolve un-der temporal constant average surface mass balance as quasi-equilibrium profiles solely by ice flow. The inland-ice vol-ume is calculated by assuming an axisymmetric ice sheet.

Vialov (1958) and also Paterson (1994), page 243, givean expression for equilibrium profiles depending on the halfspanL and the summit thicknessH as

H(x) = H

(1 −

( x

L

) n+1n

) n2(n+1)

, (A1)

wheren is the power exponent in Glen’s flow law of ice.

Fig. 9. Ice-sheet profiles for illustration of their dependence on theexponent in Glen’s law. The x-axis indicates normalized ice thick-ness and the y-axis displays the normalized horizontal expansionon an ice sheet. Typical thickness is some kilometres and typicallength some 1000 km.

Further, we can relate the summit height with the ice sheetshalf span following Paterson (1994) applying the equation

H = k√

L , (A2)

with the parameterk=3.4 (Paterson, 1994). The value fork is uncertain, what can be related to the flow properties ofice, e.g. its temperature dependence. Eq. (A2) is indepen-dent from the used power law and holds for any equilibriumprofile.

For a gross approximation of inland-ice volume, we as-sume an axisymmetric ice sheet. With Eqs. (A1) and (A2)we obtain by rotating the profile Eq. (A1) around the axisH(x=0) the integral

V = 2π k√

L

∫ L

0x(1 −

( x

L

)n+1n

) n2(n+1)

dx .

Substitution ofy=xL

, dx=L dy leads to

V = πkf L5/2 (A3)

with the abbreviation

f = 2∫ 1

0y(1 − y

n+1n

) n2(n+1)

dy . (A4)

Geometrically, one can interpretf as a form factor. Withhigher exponentsn the form factor becomes lower, becauseof the flatter edges of the profile (Fig. 9). The integral inEq. (A4) can solved with usage of0 functions according

f (ν) =40(2ν) 0

(1 +

ν2

)50(

52ν) , (A5)



Table 2. Values of the form factorf for different values of expo-nents in Glen’s flow law of ice. Two significant digits are regardedas by far accurate enough for our estimations.

n 1 2 3 . . . ∞

f 4/5 ∼0.71 ∼0.66 . . . 8/15

whereν=n/(n+1). The results for some values ofn ap-plying Eq. (A5) are summarised in Table 2. For a perfectplastic axisymmetric ice sheet (n→∞), Oerlemans (2003)found a similar expression for inland-ice volume (Eq.A3,f =8/15). Differences in the expressions are, because Oer-lemans assumed an inclined bed, while we presume a flatice-sheet base.

Further on, we adoptf (n=3)≈0.66 in our estimation, be-cause in Glen’s flow lawn=3 applies in a good approxima-tion for most parts of an ice sheet. Such a value forn isimplemented in several ice-sheet models. In particular,n=3applies in the SICOPOLIS version which is utilised in ourpaper.

Now, we have a relation between inland-ice volume andhalf span of an ice sheet (Eq.A3) together with values for allneeded constants, which will be used in the desired relationbetween inland-ice volume and time.

Total inland-ice volume is governed by the equation

dV

dt= bS , (A6)

with the inland-ice volumeV , the inland-ice areaS and theaverage surface mass balanceb. In accordance with the ax-isymmetry, the base of the ice-sheet area is assumed to bea circle

S = πL2 . (A7)

Combining Eqs. (A3), (A6) and (A7) lead to

dV

dt= π1/5b

(V

f k

)4/5

. (A8)

The differential Eq. (A8) can be integrated according

V (t) =

(π1/5b(t − t1)

5(f k)4/5+ V

1/51

)5

, (A9)

whereV1 denotes the initial inland-ice volume at timet1. Itshould be mentioned that Eq. (A9) describes the initial icespreading only. During this initial time one can assume ap-proximately constant average surface mass balance in time.It is clear that the strong power dependence with an expo-nent equal 5 in Eq. (A9) can lead to very large ice sheets ifsufficient long timet has passed. In reality, mechanism likereduction of snowfall through the elevation desert effect limitthe inland-ice volume if a large ice sheet develops. Certainly,Eq. (A9) is invalid for a mature ice sheet which can exist laterin time.

Appendix B

Equilibrium relaxation approximation

If an old ice sheet approaches equilibrium a relaxing expo-nential function is a good approximation. In the paper weuse

V (t) = (Veq − V2)(1 − exp(−(t − t2)/τ)) + V2 (B1)

to demonstrate such a relaxation effect towards an equilib-rium valueVeq with the relaxation timeτ starting with theinland-ice volumeV2 at timet2.

Acknowledgement.We would like to thank Ralf Greve for pro-viding us with the ice-sheet model SICOPOLIS. Constructivereviews of two anonymous reviewers improved the quality ofthe paper. We are grateful to the editor Richard Zeebe for hiswork with the manuscript. The authors thank Alexandra Jahn fortechnical assistance. The work was funded by a subcontract toproject 01LD0041 (DEKLIM-EEM) of the Bundesministerium furBildung und Forschung (BMBF). It was also partly funded by theDeutsche Forschungsgemeinschaft (DFG) projects CL 178/2-1 andCL 178/2-2.

Edited by: R. Zeebe

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